The present invention relates to wireless personal area networks and wireless local area networks. More particularly, the present invention relates to how to generate frequency stable wavelets for transmission in an ultrawide bandwidth device.
UWB Wavelets
UWB systems often use signals that are based on trains of short duration wavelets (also called chips or pulses) formed using a single basic wavelet shape. The interval between individual pulses can be uniform or variable, and there are a number of different methods that can be used for modulating the wavelet train with data for communications.
An important point common to UWB systems is that the individual wavelets are very short in duration, typically much shorter than the interval corresponding to a single bit of information being passed, which can offer advantages in resolving multipath components. In one embodiment, a UWB signal includes a series of wavelets formed according to the following equation:                               s          ⁡                      (            t            )                          =                              ∑                          k              =                              -                ∞                                      ∞                    ⁢                      xe2x80x83                    ⁢                                    a              k                        ⁢                          p              ⁡                              (                                  t                  -                                      t                    k                                                  )                                                                        (        1        )            
Here s(t) is the UWB signal, p(t) is the basic pulse shape, and ak and tk are the amplitude and time offset for each individual pulse. Because of the short duration of the pulses, the spectrum of the UWB signal can be several gigahertz or more in bandwidth. FIG. 1A shows an exemplary UWB wavelet.
In this example the pulse is a third derivative Gaussian wavelet with a peak-to-peak time (Tp-p) of a fraction of a fraction of a nanosecond, and a bandwidth of several gigahertz. FIG. 1B shows the frequency response of the wavelet shown in FIG. 1A.
FIG. 2 is a block diagram showing an exemplary wavelet circuit for generating the third derivative Gaussian wavelet of FIG. 1A. As shown in FIG. 2, the wavelet generating circuit 200 includes a Gaussian low pass filter 210 and first through third derivative circuits 220, 230, and 240. The Gaussian low pass filter 210 receives an impulse signal and produces a Gaussian signal p(t) as an output. This Gaussian signal p(t) is provided to the first derivative circuit 220, which outputs a first derivative Gaussian signal pxe2x80x2(t). This first derivative Gaussian signal pxe2x80x2(t) is then provided to the second derivative circuit 230, which outputs a second derivative Gaussian signal pxe2x80x3(t). Finally, the second derivative Gaussian signal pxe2x80x3(t) is provided to the third derivative circuit 240, which outputs a third derivative Gaussian signal pxe2x80x2xe2x80x3(t).
The first, second, and third derivative circuits 220, 230, and 240 are often implemented to provide approximate derivative signals. FIG. 3 is a block diagram showing an exemplary derivative circuit for generating an approximate derivative of an input signal. As shown in FIG. 3, the derivative circuit 300 includes a delay 310, an inverter 320, a summer 330, and a scaling circuit 340.
The delay 310 receives an input signal x(t) and delays it by a delay period xcfx80. The inverter 320 then inverts the delayed signal and provides it to the summer 330. The summer 330 receives the inverted delayed signal and the input signal, and adds them together, and the scaling circuit divides the sum by xcfx80.
The output of the derivative circuit 300 can thus be described by the following equation:                                           x            xe2x80x2                    ⁡                      (            t            )                          =                                            x              ⁡                              (                t                )                                      -                          x              ⁡                              (                                  t                  -                  τ                                )                                              τ                                    (        2        )            
which is an acceptable approximation of the derivative of the input signal x(t).
The wavelet output from the wavelet generating circuit 200 is used to carry data for the UWB system. Information is encoded into a series of wavelets that are wirelessly transmitted from a first device to a second device as a wireless signal.
In order to properly decode the incoming signal, the second device uses a correlation circuit. This correlation circuit allows the second device to determine the timing of an incoming signal, and the data encoded in it.
FIG. 4 is a block diagram showing a portion of a wireless receiver according to a preferred embodiment of the present invention. As shown in FIG. 4, the receiver 400 includes a pulse forming network (PFN) and timer 410 and a correlation circuit 420. The correlation circuit further includes a mixer 430 and a decision circuit.
The PFN and timer 410 preferably generates local copies of the wavelets that are the basis of the transmitted signal. (See FIG. 1A). These locally generated wavelets are provided to the correlation circuit 420 and are preferably nearly identical to the wavelets transmitted by the transmitter.
The correlation circuit 420 receives a wavelet stream that has preferably been wirelessly transmitted to the receiver 400, received at an antenna (not shown), and processed by a front end (not shown). The wavelet stream is then mixed in the mixer 430 with the locally generated wavelets to provide a correlation value.
The decision circuit receives the correlation value and uses that value to decode the information in the wavelet stream and to generate certain control signals. For example, during signal acquisition the decision circuit 440 uses the correlation value to generate control signals for the PFN and timer 410 to adjust the phase of the locally generated wavelets to match the phase of the wavelet stream. When a data signal is coming in, the decision circuit 440 uses the correlation value to decode data from the wavelet stream.
FIGS. 5A and 5B are graphs showing the autocorrelation function of the wavelet of FIG. 1A. FIG. 5A shows the autocorrelation in terms of amplitude, while FIG. 5B shows the autocorrelation in terms of dBr. Autocorrelation refers to when the wavelet is correlated with a duplicate of itself, as is done by the mixer 430 during signal acquisition.
The time axis of both of FIGS. 5A and 5B show the relative difference in wavelet starting points, delayed by the amount of time it takes for the mixer 430 to output the correlation value (a little over 400 ps in this embodiment). In the alternative, the autocorrelation graphs could be normalized to zero, setting the maximum points in the curves in FIGS. 5A ands5B at zero on the x-axis. These maximum points show where the wavelets are perfectly aligned. The remainders of the autocorrelation curves show results for varying degrees of phase shift for the two copies of the wavelet that are being autocorrelated.
However, this open loop method of generating wavelets exhibits poor frequency stability. For example, there is a significant variation in the peak-to-peak time Tp-p in wavelets depending upon temperature, component tolerances, etc. This is particularly true for the Gaussian low pass filter 210 and the delays 310 in the first, second, and third derivative circuits 220, 230, and 240. For example, the use of a delay having an LC circuit can cause a Tp-p variance of 20% by itself.
FIG. 6 is a graph showing the spectrum variance for the wavelet of FIG. 1A as its peak-to-peak time is varied. In particular, FIG. 6 shows three wavelet spectrum curves: a first spectrum curve 610 in which the peak-to-peak time Tp-p is at an ideal value, a second spectrum curve 620 in which the peak-to-peak time Tp-p is 20% below the ideal value, and a third spectrum curve 630 in which the peak-to-peak time Tp-p is 20% above the ideal value.
As shown in FIG. 6, the spectrum variance between these three curves is significant. For example, the center frequency changes from about 4.5 GHz at an ideal Tp-p up to about 7.5 GHz at xe2x88x9220% from the ideal Tp-p and down to about 3 GHz at +20% from the ideal Tp-p. This is an unacceptable variance in many UWB applications.
It is therefore desirable to provide a way of generating wavelets that have a stable frequency over a variety of conditions.
Consistent with the title of this section, only a brief description of selected features of the present invention is now presented. A more complete description of the present invention is the subject of this entire document.
An object of the present invention is to provide a method of making wavelets that have a stable frequency in a variety of environments, and a circuit for making frequency-stable wavelets.
Another object of the present invention is to provide a correlator that uses a frequency-stable wavelet generation method to achieve improved correlation performance.
These and other objects are accomplished by way of a method for generating a wavelet. This method comprises generating a first sine wave having a first frequency; generating a half sine wave window having a window frequency; and mixing the first sine wave and the half sine wave window to produce a wavelet. In this method, the window frequency is lower than the first frequency.
The half sine wave window may be a positive portion of a sine wave from 0 to 180 degrees, or a negative portion of a sine wave from 180 to 360 degrees. The first frequency is preferably between two and four times the window frequency, and more preferably three times the window frequency.
The step of generating a half sine wave window may further comprise generating a second sine wave having a second frequency; and fully rectifying the second sine wave to form the half sine wave window. In this step, the second frequency is twice the window frequency.
The first and second sine waves are each preferably generated using a phase locked loop circuit.
Also provided is a wavelet generator, comprising: a first sine wave generator for generating a first sine wave having a first frequency; a half sine wave window generator for generating a half sine wave window having a window frequency; and a mixer for mixing the first sine wave and the half sine wave window to produce a wavelet. In this wavelet generator, the window frequency is lower than the first frequency.
The first frequency is preferably between two and four times the window frequency, and more preferably three times the window frequency.
The half sine wave window generator may further comprise a second sine wave generator for generating a second sine wave having a second frequency; a full wave rectifier for fully rectifying the second sine wave to form the half sine wave window the second frequency is twice the window frequency.
The first and second sine wave generators are preferably each phase locked loop circuits.
A method for generating wavelets is also provided. This method comprises generating a first sine wave having a first frequency; generating a series of half sine wave windows, having a window frequency; and mixing the first sine wave and the half sine wave windows to produce a series of wavelets. In this method the window frequency is lower than the first frequency.
The first frequency is preferably between two and four times the window frequency, and more preferably three times the window frequency.
The step of generating a half sine wave window may further comprise: generating a second sine wave having a second frequency; and fully rectifying the second sine wave to form the series of half sine wave windows. In this method, the second frequency is twice the window frequency.
The first and second sine waves are preferably each generated using a phase locked loop circuit.
A method is also provided for correlating incoming wavelets with locally generated wavelets. This method comprises: generating a first sine wave having a first frequency; generating a series of half sine wave windows, having a window frequency; mixing the first sine wave and the half sine wave windows to produce a locally-generated wavelet stream; receiving an incoming wavelet stream; and mixing the locally-generated wavelet stream with the incoming wavelet stream to generate a correlation value. In this method, the window frequency is lower than the first frequency.
The first frequency is preferably between two and four times the window frequency, and more preferably three times the window frequency.
The step of generating a half sine wave window may further comprise: generating a second sine wave having a second frequency; and fully rectifying the second sine wave to form the series of half sine wave windows. In this step, the second frequency is twice the window frequency.
The first and second sine waves are preferably each generated using a phase locked loop circuit.
A correlator is also provided, comprising: a first sine wave generator for generating a first sine wave having a first frequency; a second sine wave generator for generating a second sine wave having a second frequency; a half sine wave window generator for generating a series of half sine wave windows having a window frequency; a first mixer for mixing the first sine wave and the series of half sine wave windows to produce a locally-generated wavelet stream; and a second mixer for mixing the locally-generated wavelet stream with an incoming wavelet stream to generate a correlation value. In this correlator, the second frequency is lower than the first frequency.
The first frequency is preferably between two and four times the window frequency, and more preferably three times the window frequency.
The half sine wave window generator may further comprise: a second sine wave generator for generating a second sine wave having a second frequency; and a full wave rectifier for fully rectifying the second sine wave to form the series of half sine wave windows. In the half sine wave window generator, the second frequency is twice the window frequency.
The first and second sine waves are preferably each generated using a phase locked loop circuit.